A Rotating vacuum and the quantum Mach's principle

In this work we consider a quantum analog of Newton's bucket experiment in a flat spacetime: we take an Unruh-DeWitt detector in interaction with a real massless scalar field. We calculate the detector's excitation rate when it is uniformly rotating around some fixed point and the field is prepared in the Minkowski vacuum and also when the detector is inertial and the field is in the Trocheries-Takeno vacuum state. These results are compared and the relations with a quantum analog of Mach's principle are discussed.